5n-2n(n-2)=-11

Solution for 5n-2n(n-2)=-11 equation:

5n-2n(n-2)=-11

We move all terms to the left:

5n-2n(n-2)-(-11)=0

We add all the numbers together, and all the variables

5n-2n(n-2)+11=0

We multiply parentheses

-2n^2+5n+4n+11=0

We add all the numbers together, and all the variables

-2n^2+9n+11=0

a = -2; b = 9; c = +11;
Δ = b2-4ac
Δ = 92-4·(-2)·11
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-13}{2*-2}=\frac{-22}{-4}
=5+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+13}{2*-2}=\frac{4}{-4}
=-1
$